Quantum-resistant cryptographic algorithms grounded in discrete mathematical foundations

Mane, Vikramsinha V.; Jagtap, Mahesh P.; Dhamone, Santosh Shivlal; Raut, Avinash B.; Wanjale, Kirti; Makhmudov, Samariddin

doi:10.47974/JDMSC-2519

Open Access Research Article

Quantum-resistant cryptographic algorithms grounded in discrete mathematical foundations

Vikramsinha V. Manevvmosmanabad@gmail.comDepartment of Mechanical EngineeringTerna Public Charitable Trust’s College of EngineeringOsmanabad, Maharashtra, 413501, IndiaView full profile → , ^*Mahesh P. JagtapCorresponding authormaheshmaths@gmail.comDepartment of MathematicsPimpri Chinchwad UniversityPune, Maharashtra, 412106, IndiaView full profile → , Santosh Shivlal Dhamonesantosh2maths@gmail.comDepartment of MathematicsSGV&SSP’s, Arts Commerce and Science CollegePalghar, Maharashtra, 40105, IndiaView full profile → , Avinash B. Rautavinash.raut@vit.eduDepartment of Engineering, Science and HumanitiesVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Kirti Wanjalekirti.wanjale@vit.eduDepartment of Computer EngineeringVishwakarma Institute of TechnologyPune, Maharashtra, 411037, IndiaView full profile → , Samariddin Makhmudovsamariddin_maxmudov@tues.uz maxmudov_samariddin@mamunedu.uz s.makhmudov@tsue.uzAffiliation 1Department of Finance and TourismTermez University of Economics and ServiceTermez, UzbekistanAffiliation 2Department of EconomicsMamun UniversityKhiva, 220900, UzbekistanAffiliation 3Center of the Engagement of International Ranking AgenciesTashkent State University of EconomicsTashkent, UzbekistanView full profile →

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pp. 731–739Vol. 29Issue 2-AFebruary 2026DOI: 10.47974/JDMSC-2519 Crossmark XML

Received:: 07 May 2025
Published Online:: 31 Dec 2025
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2519
Pages:: 731–739

Abstract

Classical encryption algorithms are in serious danger from quantum computing, so new algorithms that can’t be broken by quantum computers need to be made. This essay looks at discrete mathematical concepts that are important for making these kinds of algorithms. It mainly talks about number theory, lattice theory, and coding theory. We look at both code-based and lattice-based cryptographic methods, which look like good options for security after quantum computing. There are hardness assumptions that can’t be broken by quantum attacks in lattice problems like the smallest vector problem, and error-correcting codes are the basis of code-based cryptosystems that have been shown to be strong. We provide a strict framework that makes these quantum-resistant algorithms safer and more efficient by using vector measure spaces, orthogonal sets, and sequences.

Keywords

Quantum-resistant cryptography Lattice theory Coding theory Number theory Vector metric space

Subject Classifications

31A1033E30

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